As many as 35 were also wounded in the attack, which took place in the Dahyan market in Saada province, a stronghold of the rebels known as Houthis, the elders said.
"We call on the Saudi-led coalition to conduct a thorough and transparent investigation into the incident", she said.
Footage from the Houthi media office showed a boy wearing a blue backpack with a UNICEF logo being carried into a hospital emergency room with blood pouring down his face and over his traditional Yemeni thawb, an ankle-length garment.
"Targeting Saudis and residents in Saudi is a red line", coalition spokesman Turki al-Malki later told Al Arabiya TV. This action is in conformity with the humanitarian law, Saudi Press Agency (SPA) quoted Col.
The International Committee of the Red Cross said it was sending supplies to ICRC-supported hospitals to support an influx of casualties.
"The secretary general condemns the airstrike today by the coalition forces in Sa'ada, which hit a busy market area in Majz district and impacted a bus carrying children from a summer camp", Farhan Haq, the United Nations chief's deputy spokesman, said in a statement on Thursday.
The children were reportedly on a field trip, when their bus was hit by an airstrike.
It was there, as the students sat waiting to resume their journey home on Thursday, that a Saudi-led coalition airstrike hit their school bus.
Yemeni tribal leaders told the AP the Saudi-led USA -backed coalition fighting Shiite Houthi rebels was behind the airstrike.More news: PS4 Pro is getting a 500 Million Limited Edition release
"Shrapnel from the intercepted missile scattered over residential areas, leaving a Yemeni resident killed and 11 other civilians wounded", the coalition said.
He stressed that the Houthi leaders and terrorist elements responsible for firing ballistic missiles and targeting civilians will be targeted as part of the coalition efforts to prevent terrorist elements from harming regional and global security.
He added: "Launching ballistic missiles at densely-populated civilian areas is a direct breach of the principles of worldwide humanitarian law".
The Houthis seized the capital, Sanaa, in 2014 and overthrew the internationally recognised government led by President Abdrabu Mansur Hadi during a transition of power from former president Ali Abdullah Saleh. The coalition denied that it had carried out air strikes in the area, and blamed the deaths on rebel mortar fire.
Worldwide rights groups repeated calls for an end to the war and strongly condemned the bus attack and other civilian massacres.
Yemen's war has left almost 10,000 people dead since 2015 and unleashed what the United Nations describes as the world's worst humanitarian crisis.
"It is beyond cruel; innocent children's lives have been lost".
He added that as a result of Trump's "strong and positive signals", Iranian-backed Houthi rebels are beginning to engage more with the peace process and said, "So withdrawing from the Iran deal will definitely contribute to the end of the war in Yemen".